where \(\alpha \)  and \(\beta \)  are the self-similar exponents being real numbers describing the decay and the spreading of the solution is time and space.
These properties makes this Ansatz physically extraordinary relevant and was first introduced by
Sedov [1]} later used by Zel'dowich and Raizer [2]} and Barenblatt [3]}.
In the last decade we applied this trial function to numerous non-linear PDE systems, most of them are from fluid dynamics [4]} but
investigated electromagnetic [5]} or quantum mechanical problems [6]} as well.
The self-similar analysis have been successfully applied to different systems, where diffusion may also appear [7]}, [8]}, [9]}.
